# Proper Pricing Approach to the Water Supply Cost Sharing: A Case Study of the Eastern Route of the South to North Water Diversion Project in China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

#### 2.2. Methods

#### 2.2.1. Existing Cost-Sharing Method

_{n}is the sharing cost of nth water intake; S

_{in}is the water supply cost of the ith section, shared by the nth water intake in accordance with the amortized water quantity in proportion; C

_{n}is the water supply cost of the nth section; W

_{n}is the net quantity of water supply for the nth section, in million cubic meters (MCM); K

_{n}is the water supply costs of the nth section, in million RMB; m is the total number of users.

_{n}is UWSC of the nth section, RMB/m

^{3}.

#### 2.2.2. Improved Cost-Sharing Method

_{i}is the amount of water withdrawn by the ith section. α is the correction coefficient. When the water intake users are evenly distributed along the line, the correction coefficient α can be easily proven to be 0.5.

#### 2.2.3. ICSM for Branch Route

## 3. Results

#### 3.1. Comparison of the UWSC between CAF and ICSM in the Different Scenarios

#### 3.2. Analysis of Mathematical Characteristics of CAF and ICSM

- (1)
- CAF

_{i}= C and W

_{i}= W. According to Equations (1) and (2), the general expression of the UWSC of the nth user (D

_{n}) based on CAF can be derived as:

_{n}is the UWSC of the nth section, C

_{Tm}and W

_{Tm}are the cost and water supply of a single section.

_{n}) still change nonlinearly with the increase in the total number of users.

- (2)
- ICSM

_{n}based on ICSM is derived by using Equations (4) and (5), shown in Equation (9). It shows that D

_{n}will be a constant value when n approaches infinity, i.e., D

_{n}= 2C/W, under the condition that n is no larger than m. This illustrates that the formula of ICSM is a convergent function and the UWSC in the last section (the nth section) is double the average unit water supply costs of the entire water supply route:

_{n}is the UWSC of the nth section, m is the number of total sections of the whole route, and n is the number of calculated sections.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Madani, K. Game theory and water resources. J. Hydrol.
**2010**, 381, 225–238. [Google Scholar] - Shuai, J.; Cheng, X.; Ding, L.; Yang, J.; Leng, Z. How should government and users share the investment costs and benefits of a solar PV power generation project in China? Renew. Sustain. Energy Rev.
**2019**, 104, 86–94. [Google Scholar] [CrossRef] - Banovec, P.; Domadenik, P. Paying too much or too little? Pricing approaches in the case of cross-border water supply. Water Sci. Technol. Water Supply
**2018**, 18, 577–585. [Google Scholar] [CrossRef] - Chen, Z.; Cheung, K.C.; Tan, M. Inter-Basin Water Transfer Supply Chain Coordination with Ramsey Pricing. Int. J. Environ. Res. Public Health
**2019**, 16, 3651. [Google Scholar] [CrossRef] [PubMed] - Ballestero, E. Inter-basin water transfer public agreements: A decision approach to quantity and price. Water Resour. Manag.
**2004**, 8, 75–88. [Google Scholar] [CrossRef] - Sechi, G.M.; Zucca, R.; Zuddas, P. Water costs allocation in complex systems using a cooperative game theory approach. Water Resour. Manag.
**2013**, 27, 1781–1796. [Google Scholar] [CrossRef] - Du, W.; Fan, Y.; Tang, X. Two-part pricing contracts under competition: The South-to-North Water Transfer Project supply chain system in China. Int. J. Water Resour. Dev.
**2016**, 32, 895–911. [Google Scholar] [CrossRef] - Young, H.P.; Okada, N.; Hashimoto, T. Cost allocation in water resources development. Water Resour. Res.
**1982**, 18, 463–475. [Google Scholar] [CrossRef] - Garcia, S.; Thomas, A. The structure of municipal water supply costs: Application to a panel of French local communities. J. Product. Anal.
**2001**, 16, 5–29. [Google Scholar] [CrossRef] - Janjua, S.; Hassan, I. Transboundary water allocation in critical scarcity conditions: A stochastic bankruptcy approach. J. Water Supply Res. Technol. AQUA
**2020**, 69, 224–237. [Google Scholar] [CrossRef] - Jafarzadegan, K.; Abed-Elmdoust, A.; Kerachian, R. A stochastic model for optimal operation of inter-basin water allocation systems: A case study. Stoch. Environ. Res. Risk Assess.
**2014**, 28, 1343–1358. [Google Scholar] [CrossRef] - Proag, V. Cost Allocation for Infrastructure Implementation. In Infrastructure Planning and Management: An Integrated Approach; Springer: Cham, Switzerland, 2021; pp. 535–561. [Google Scholar]
- Massoud, T.G. Fair division, adjusted winner procedure (AW), and the Israeli-Palestinian conflict. J. Confl. Resolut.
**2000**, 44, 333–358. [Google Scholar] [CrossRef] - Losa, F.B.; Van Den Honert, R.; Joubert, A. The multivariate analysis biplot as tool for conflict analysis in MCDA. J. Multi-Criteria Decis. Anal.
**2001**, 10, 273–284. [Google Scholar] [CrossRef] - Giordano, R.; Passarella, G.; Uricchio, V.F.; Vurro, M. Fuzzy cognitive maps for issue identification in a water resources conflict resolution system. Phys. Chem. Earth Parts A/B/C
**2005**, 30, 463–469. [Google Scholar] [CrossRef] - Chhipi, S.G.; Rodriguez, M.; Sadiq, R. Selection of sustainable municipal water reuse applications by multi-stakeholders using game theory. Sci. Total Environ.
**2019**, 650, 2512–2526. [Google Scholar] [CrossRef] - Pohlner, H. Institutional change and the political economy of water mega projects: China’s south-north water transfer. Glob. Environ. Change
**2016**, 38, 205–216. [Google Scholar] [CrossRef] - Chen, Z.; Wang, H.; Qi, X. Pricing and water resource allocation scheme for the south-to-north water diversion project in China. Water Resour. Manag.
**2013**, 27, 1457–1472. [Google Scholar] [CrossRef] - Liu, Y.; Mark, W.; Michael, W.; Zhou, C.; Zhang, W. Alternative water supply solutions: China’s South-to-North-water-diversion in Jinan. J. Environ. Manag.
**2020**, 276, 111337. [Google Scholar] [CrossRef] - Li, N.; Zheng, C. Water Supply Cost-Sharing of SNWTP. In Proceedings of the 2010 Asia-Pacific Power and Energy Engineering Conference, Chendu, China, 28–31 March 2010; pp. 1–4. [Google Scholar]
- Ministry of Water Resources. Specification for Economic Evaluation of Water Conservancy Construction Projects. Available online: http://hbba.sacinfo.org.cn/stdDetail/48b69394191475dbc3b345bdcb03f6b5 (accessed on 20 August 2022).
- Wang, M.; Li, C. An institutional analysis of China’s South-to-North water diversion. Thesis Elev.
**2019**, 150, 68–80. [Google Scholar] [CrossRef] - Jiang, M.; Webber, M.; Barnett, J.; Rogers, S.; Rutherfurd, I.; Wang, M.; Finlayson, B. Beyond contradiction: The state and the market in contemporary Chinese water governance. Geoforum
**2020**, 108, 246–254. [Google Scholar] - Kattel, G.; Reeves, J.; Western, A.; Zhang, W.; Jing, W.; McGowan, S.; Cuo, L.; Scales, P.; Dowling, K.; He, Q.; et al. Healthy waterways and ecologically sustainable cities in Beijing-Tianjin-Hebei urban agglomeration (northern China): Challenges and future directions. Wiley Interdiscip. Rev. Water
**2021**, 8, e1500. [Google Scholar] [CrossRef] - Li, H. Evolutionary game analysis of emergency management of the Middle Route of South-to-North Water Diversion Project. Water Resour. Manag.
**2017**, 31, 2777–2789. [Google Scholar] - Chen, D.; Luo, Z.; Webber, M.; Rogers, S.; Rutherfurd, I.; Wang, M.; Finlayson, B.; Jiang, M.; Shi, C.; Zhang, W. Between project and region: The challenges of managing water in Shandong province after the south-north water transfer project. Water Altern.
**2020**, 13, 49–69. [Google Scholar] - Xue, C.; Chen, Z. Joint pricing and inventory management of interbasin water transfer supply chain. Complexity
**2020**. [Google Scholar] [CrossRef]

**Figure 4.**The route diagram of the ER- SNWDP in this paper (Sec. 1 represents the first section of the ER-SNETP, which is from Hongze Lake to Luoma Lake, as shown in Table 1, Section 2–Section 6(2) follow the same structure).

**Figure 5.**Comparisons of the UWSC between CAF and ICSM in different scenarios. (The dotted line indicates the dividing line between upstream and downstream; the four subfigures represent results for scenarios #1–4).

**Figure 6.**The comparison of UWSC between CAF and ICSM when the number of water intake locations is 30 and the total section numbers range from 1 to 30. (

**a**) is the UWSC of CAF, (

**b**) is the UWSC of ICSM.

Section 1 | Section 2 | Section 3 | Section 4 | Section 5 | Section 6-1 | Section 6-2 | |
---|---|---|---|---|---|---|---|

Investment (million RMB *) | 349.9 | 87.4 | 137.1 | 101.3 | 186.5 | 251.5 | 415.9 |

Net quantity (MCM) | 391 | 447 | 244 | 300 | 0 | 379 | 746 |

No. of Sections | CAF | SW-WCQ | |||
---|---|---|---|---|---|

C_{n}(million RMB) | D_{n}(RMB/m³) | C(1, n) (million RMB) | W(1, n) (MCM) | D(n) (RMB/m³) | |

Section 1 | 349.9 | 0.1396 | 349.9 | 391.0 | 0.1496 |

Section 2 | 87.4 | 0.1809 | 437.3 | 838.0 | 0.2037 |

Section 3 | 137.1 | 0.2630 | 574.4 | 1082.0 | 0.2813 |

Section 4 | 101.3 | 0.3341 | 675.7 | 1382.0 | 0.3531 |

Section 5 | 186.5 | 0.4999 | 862.2 | 1382.0 | 0.4506 |

Section 6-1 (BR1) | 251.5 | 1.1635 | 1113.7 | 1761.0 | 1.1085 |

Section 6-2 (BR2) | 415.9 | 1.0574 | 1278.1 | 2128.0 | 1.0528 |

Sections | Transferred Water Volume (MCM) | The Differences between CAF and ICSM (Million RMB) | |
---|---|---|---|

Scenario #1 | Section 1 | 391.00 | 3.92 |

Section 2 | 447.00 | 10.19 | |

Section 3 | 244.00 | 4.45 | |

Section 4 | 300.00 | 5.71 | |

Section 5 | 0.00 | 0.00 | |

Section 6-1 | 379.00 | −20.82 | |

Section 6-2 | 746.00 | −3.44 | |

Scenario #2 | Section 1 | 391.00 | 3.84 |

Section 2 | 447.00 | 9.92 | |

Section 3 | 544.00 | 14.94 | |

Section 4 | 0.00 | 0.00 | |

Section 5-1 | 379.00 | −22.49 | |

Section 5-2 | 746.00 | −6.17 | |

Scenario #3 | Section 1 | 391.00 | 3.85 |

Section 2 | 447.00 | 9.95 | |

Section 3 | 544.00 | 15.08 | |

Section 4 | 0.00 | 0.00 | |

Section 5 | 1125.00 | −28.89 | |

Scenario #4 | Section 1 | 838.00 | 23.44 |

Section 2 | 544.00 | 17.30 | |

Section 3 | 0.00 | 0.00 | |

Section 4 | 1125.00 | −40.70 |

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**MDPI and ACS Style**

Liu, Y.; Chong, F.; Jia, J.; Cao, S.; Wang, J.
Proper Pricing Approach to the Water Supply Cost Sharing: A Case Study of the Eastern Route of the South to North Water Diversion Project in China. *Water* **2022**, *14*, 2842.
https://doi.org/10.3390/w14182842

**AMA Style**

Liu Y, Chong F, Jia J, Cao S, Wang J.
Proper Pricing Approach to the Water Supply Cost Sharing: A Case Study of the Eastern Route of the South to North Water Diversion Project in China. *Water*. 2022; 14(18):2842.
https://doi.org/10.3390/w14182842

**Chicago/Turabian Style**

Liu, Yang, Fatong Chong, Jingjing Jia, Shengle Cao, and Jun Wang.
2022. "Proper Pricing Approach to the Water Supply Cost Sharing: A Case Study of the Eastern Route of the South to North Water Diversion Project in China" *Water* 14, no. 18: 2842.
https://doi.org/10.3390/w14182842